Research On Quantum Entanglement And Quantum Coherence Based On Measurement And Channel

Quantum entanglement and quantum coherence are not only the basic characteristics of quantum mechanics that are different from classical mechanics but also important resources for realizing quantum information processing tasks such as quantum computing and quantum secure communication.It is also a hotspot in the research of quantum information theory.In this thesis,quantum entanglement characterizations based on measurement,quantum coherence based on channel and quantum coherence estimation problems are systematically studied by using the theories and methods of operator theory and matrix theory.This thesis is divided into six chapters,and the main contents are as follows.In Chapter 1,we introduce some research background,research significance and research status on our main contents,and give the main results in this thesis.In Chapter 2,firstly,we review some of the basic linear algebra used in quantum mechanics and then introduce the relevant basic knowledge of quantum information theory.Secondly,the definition of free state and free operation in the theory of entanglement and coherence in quantum resource theory,the quantifying framework of entanglement and coherence,and some commonly used coherence measures are introduced.Finally,the applications of quantum coherence in different fields are introduced.In Chapter 3,we study the measurement-based entanglement characterizations and the relationship among quantum entanglement,Bell nonlocality,steerability and quantum correlation in bipartite systems.Firstly,we have obtained the characterization of entanglement of quantum states under POVM measurements.Secondly,using Bell local inequality,it is proved that when the dimensions of the two systems are the same,pure states are separable if and only if it is Bell local.When the dimensions of two systems are different,the separability of the pure states is the same as the Bell locality,and the Bell locality characterization of the pure state based on projection measurements is otained.Then,by the mathematical characterization of the bipartite quantum state that is unsteerable,It is obtained that the pure state is entangled if and only if it is two-way steerable.Finally,we have proved that the separability of the pure state is the same as the classical correlation.Consequently,every entangled pure bipartite state is always Bell nonlocal,two-way steerable and quantum correlated.In Chapter 4,we study channel-based quantum coherence.Firstly,we have introduced the concept of ?-coherence and established some basic properties of?-incoherence including a series of examples,and proved that the convexity and compactness of all sets of ?-incoherent states.Secondly,we have generalized the usual incoherent operations to the ?-incoherent operations(?-IOs)and proved that the set IO(?)of all ?-IOs of H is a nonempty convex set.We have also established some characterizations of ?-IOs.Finally,we have proposed the concept of a ?coherence measure and introduced two types of ?-coherence measures.At the same time,the uncertainty relation of relative entropy measure C??re is obtained.In Chapter 5,we study the estimation problems of the coherence measure.Firstly,based on the quantifying framework of coherence measure,it is obtained that any two mixed forms of coherence measure are also a coherence measure.Secondly,the upper bound and lower bound of the relative entropy coherence of any quantum state on the tripartite systems are obtained.Then,using mathematical induction,it is extended to an n-partite case,and we have established lower and upper bounds for relative entropy of coherence for multipartite systems.An example is given to show that the inequality given is compact.Finally,the relationship between l1norm coherence measure and relative entropy coherence measure are discussed,and another simple proof that any single qubit mixed state satisfies Cre(?)?C(?)l(p)is given.In Chapter 6,we summarize the research results obtained in this thesis and prospect the future research.